Vibrations of an elastic plate partially immersed in a liquid

The free vibrations of an elastic plate, placed orthogonally at the bottom of an unbounded open reservoir of constant depth, are considered. The reservoir is filled with a compressible liquid, the plate protrudes above the free surface and its rigidly fastened to the bottom. Gravitational effects are ignored. An analytical representation of the acoustic field in the liquid and the vibrational field in the plate is obtained. The natural frequencies and natural forms of vibration are calculated as a function of the height of the liquid level. An approximate approach to calculating the vibrations of the plate is considered.